Escape Velocity

v = \sqrt{\frac{2GM}{r}}

v =

M =

r =

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

Constant used — built into this formula, no need to enter

G = 6.6743 \times 10^{-11}\ \text{m}^{3}\text{/(kg}{\cdot}\text{s}^{2}\text{)}

Newtonian constant of gravitation

Learning zone

Escape velocity comes from an energy balance: launch with kinetic energy ½mv² at least equal to the gravitational well's depth GMm/r, and the projectile coasts to infinity with nothing to spare. The projectile's own mass cancels, and the direction of launch doesn't matter — only the speed. For Earth, v = √(2 × 6.674 × 10⁻¹¹ × 5.97 × 10²⁴ / 6.371 × 10⁶) ≈ 11 190 m/s, the familiar 11.2 km/s that every Moon-bound Apollo mission had to approach.

Note the √2: escape speed is exactly √2 times circular orbital speed at the same radius. The formula also sorts the solar system's atmospheres — the Moon's gentle 2.4 km/s could not hold onto gas molecules, while Jupiter's crushing 59.5 km/s keeps even hydrogen. Push the logic to its limit by asking where escape velocity reaches the speed of light, and you arrive at the Schwarzschild radius of a black hole.

Escape Velocity

v = \sqrt{\frac{2GM}{r}}

Where

$v$ = Escape velocity
$M$ = Central mass
$r$ = Starting distance

Missing one of these? Work it out first, then come back

Escape velocity — Linear Momentum (p = mv), Power from Force and Velocity (P = Fv)
Central mass — Orbital Velocity, Orbital Period
Starting distance — Speed, Distance & Time, Gravitational Field Strength

Part of this formula set

Gravitation and orbital mechanics

8 formulasNewton's inverse-square law and what falls out of it in orbit — field strength, orbital speed and period, Kepler's third law, and escape velocity.